Question

how many bushels will the bin in the figure hold? (1 cu ft ≈ 1.24 bushels.)
the bin in the figure will hold approximately bushels.
(simplify your answer. type an integer or a decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Identify the shape and formula

The bin is a frustum of a cone (or a truncated cone). The volume \( V \) of a frustum of a cone is given by the formula \( V=\frac{1}{3}\pi h (R^{2}+Rr + r^{2}) \), where \( h \) is the height of the frustum, \( R \) is the radius of the larger base, and \( r \) is the radius of the smaller base. From the figure, the larger diameter is \( 14 \) ft, so \( R=\frac{14}{2}=7 \) ft. The smaller diameter is \( 8 \) ft, so \( r = \frac{8}{2}=4 \) ft. The height \( h = 9 \) ft.

Step2: Calculate the volume of the frustum

Substitute \( R = 7 \), \( r = 4 \), and \( h=9 \) into the formula:

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Using \( \pi\approx3.1416 \), we get \( V\approx279\times3.1416\approx876.5784 \) cubic feet.

Step3: Convert cubic feet to bushels

We know that \( 1 \) cubic foot \( \approx1.24 \) bushels. So, the number of bushels \( B=876.5784\times1.24 \).

$$ B\approx876.5784\times1.24 = 1086.957216 $$

Answer:

\( 1087.0 \) (rounded to the nearest tenth) or \( 1087 \) (as an integer)